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March 12th, 2010, 10:34 AM  #1 
Newbie Joined: Mar 2010 Posts: 7 Thanks: 0  I can't understand this proof about Uniform Structures
There is a uniform structure U, defining a uniform topology associated with U. For every U U, U[x] is U evaluated at x, and U[A] is the union of U evaluated at every point in A. The theorem is: U[A] B for some U, then The proof is below: We may suppose that U is symmetric since there is a symmetric V such that V[A] (I don't understand how we can conclude that U is symmetric based on the fact that it has a symmetric subset; I understand the rest of the proof.) (by symmetry of U) (implies closure of A is in B) I figured this out, instead of U, use the arguments on the symmetric V. V[a] is a subset of U[a]. 

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proof, structures, understand, uniform 
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